Example

Multiplying (x+3)(x+7)(x + 3)(x + 7) Using the Distributive Property

Multiply (x+3)(x+7)(x + 3)(x + 7) by applying the Distributive Property twice.

Step 1 — Treat (x+7)(x + 7) as a single unit and distribute it: Imagine that (x+7)(x + 7) plays the same role a monomial pp would in the expression (x+3)p(x + 3) \cdot p. Distribute (x+7)(x + 7) to each term of the first binomial:

x(x+7)+3(x+7)x(x + 7) + 3(x + 7)

Step 2 — Distribute again within each product: Multiply xx by each term in (x+7)(x + 7), and multiply 33 by each term in (x+7)(x + 7):

x2+7x+3x+21x^2 + 7x + 3x + 21

This produces four terms — one for each pair of terms from the two binomials.

Step 3 — Combine like terms: The middle terms 7x7x and 3x3x are like terms: 7x+3x=10x7x + 3x = 10x:

x2+10x+21x^2 + 10x + 21

The result is x2+10x+21x^2 + 10x + 21. Replacing a monomial factor with a binomial factor simply introduces one additional round of distribution — the same Distributive Property is applied twice in succession.

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Updated 2026-04-29

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